Union symbol (∪)

How to read it

OpenStax’s Contemporary Mathematics defines A ∪ B as {x | x ∈ A or x ∈ B} and calls union a logical inclusive OR: an element is in the union if it is in the first set, the second, or both. Elements in both sets are listed once: in OpenStax’s example, 3, 5 and 7 belong to both sets and appear once in the union {1, 3, 5, 7, 9, 2}. Oscar Levin’s Discrete Mathematics gives the same definition. Because shared elements count once, the sizes don’t simply add: OpenStax gives n(A ∪ B) = n(A) + n(B) − n(A ∩ B), taking off the Intersection symbol (∩) that would otherwise be counted twice. Unicode names the character UNION (U+222A), also called cup, and has a larger n-ary form ⋃ (U+22C3) for the union of many sets.

Also searched as: ∪, A ∪ B, cup symbol, union of sets, u symbol in math.

∪ and ∨

The union sign is a rounded cousin of ∨, the logical “or”, and means much the same thing for sets: x is in A ∪ B when x ∈ A ∨ x ∈ B. Its opposite is the intersection ∩, the same shape upside down.